Backpacking in the Alps

I'm thinking about backpacking in the Alps, doing a week or so hut to hut. I'm a moderately experienced backpacker, and I've just returned from the Camino de Santiago. Ideally I would like to spend one day in the city I fly into, and I'm actually pretty indifferent as to where I go. Does anyone have any suggestions on a good week-long, hut-to-hut-to-hut hike that begins and ends in towns that are easily rail accessible? Obviously virtually everywhere in Europe is rail-accessible, but I'd like to minimize time traveling in order to maximize time hiking. Even better if I can fly out of my final town or city back to a major international airport. Thanks!